论文标题
liouville域的光谱直径
The spectral diameter of a Liouville domain
论文作者
论文摘要
由于Viterbo，Schwarz，Oh，Frauenfelder和Schlenk，由自然双向歧管的紧凑型汉密尔顿的差异性赋予了自然的双向距离，来自汉密尔顿Floer同源性的光谱不变。这个距离在符号拓扑中发现了许多应用。但是，总体上仍然未知其直径。实际上，对于封闭的符号歧管，直径是无限的统一标准。在本文中，我们证明，对于任何liouville领域，此直径是无限的，并且仅当它的符号共同体学不会消失时。这概括了Monzner-Vichery-Zapolsky的结果，并在封闭的符号歧管的设置中应用。
The group of compactly supported Hamiltonian diffeomorphisms of a symplectic manifold is endowed with a natural bi-invariant distance, due to Viterbo, Schwarz, Oh, Frauenfelder and Schlenk, coming from spectral invariants in Hamiltonian Floer homology. This distance has found numerous applications in symplectic topology. However, its diameter is still unknown in general. In fact, for closed symplectic manifolds there is no unifying criterion for the diameter to be infinite. In this paper, we prove that for any Liouville domain this diameter is infinite if and only if its symplectic cohomology does not vanish. This generalizes a result of Monzner-Vichery-Zapolsky and has applications in the setting of closed symplectic manifolds.
